HDU1281-棋盘游戏-二分图匹配

Posted 2020-08-05 Helica

先跑一个二分图匹配，然后一一删去匹配上的边，看能不能达到最大匹配数，不能这条边就是重要边

  1 /*--------------------------------------------------------------------------------------*/
  2 
  3 #include <algorithm>
  4 #include <iostream>
  5 #include <cstring>
  6 #include <ctype.h>
  7 #include <cstdlib>
  8 #include <cstdio>
  9 #include <vector>
 10 #include <string>
 11 #include <queue>
 12 #include <stack>
 13 #include <cmath>
 14 #include <set>
 15 #include <map>
 16 
 17 //debug function for a N*M array
 18 #define debug_map(N,M,G) printf("\n");for(int i=0;i<(N);i++) 19 {for(int j=0;j<(M);j++){ 20 printf("%d",G[i][j]);}printf("\n");}
 21 //debug function for int,float,double,etc.
 22 #define debug_var(X) cout<<#X"="<<X<<endl;
 23 #define LL long long
 24 const int INF = 0x3f3f3f3f;
 25 const LL LLINF = 0x3f3f3f3f3f3f3f3f;
 26 /*--------------------------------------------------------------------------------------*/
 27 using namespace std;
 28 
 29 int N,M,E,T;
 30 const int maxn = 1000;
 31 vector <int> G[maxn];
 32 int uN;
 33 int Mx[maxn],My[maxn];
 34 int dx[maxn],dy[maxn];
 35 int dis;
 36 bool used[maxn];
 37 bool searchP()
 38 {
 39     queue<int> Q;
 40     dis = INF;
 41     memset(dx,-1,sizeof dx);
 42     memset(dy,-1,sizeof dy);
 43     for(int i=1;i<=uN;i++)
 44     {
 45         if(Mx[i] == -1)
 46         {
 47             Q.push(i);
 48             dx[i] = 0;
 49         }
 50     }
 51     while(!Q.empty())
 52     {
 53         int u = Q.front();
 54         Q.pop();
 55         if(dx[u] > dis) break;
 56         int sz = G[u].size();
 57         for(int i=0;i<sz;i++)
 58         {
 59             int v = G[u][i];
 60             if(dy[v] == -1)
 61             {
 62                 dy[v] = dx[u] + 1;
 63                 if(My[v] == -1) dis = dy[v];
 64                 else
 65                 {
 66                     dx[My[v]] = dy[v] + 1;
 67                     Q.push(My[v]);
 68                 }
 69             }
 70         }
 71     }
 72     return dis != INF;
 73 }
 74 bool DFS(int u)
 75 {
 76     int sz = G[u].size();
 77     for(int i=0;i<sz;i++)
 78     {
 79         int v = G[u][i];
 80         if(!used[v] && dy[v] == dx[u]+1)
 81         {
 82             used[v] = true;
 83             if(My[v] != -1 && dy[v] == dis) continue;
 84             if(My[v] == -1 || DFS(My[v]))
 85             {
 86                 My[v] = u;
 87                 Mx[u] = v;
 88                 return true;
 89             }
 90         }
 91     }
 92     return false;
 93 }
 94 int MaxMatch()
 95 {
 96     int res = 0;
 97     memset(Mx,-1,sizeof Mx);
 98     memset(My,-1,sizeof My);
 99     while(searchP())
100     {
101         memset(used,false,sizeof used);
102         for(int i=1;i<=uN;i++)
103         {
104             if(Mx[i] == -1 && DFS(i)) res++;
105         }
106     }
107     return res/2;
108 }
109 
110 vector <pair<int,int> > save;
111 set <pair<int,int> > st;
112 int cas;
113 int main()
114 {
115     while(~scanf("%d%d%d",&N,&M,&E))
116     {
117         uN = N+M;
118         for(int i=0;i<maxn;i++) G[i].clear();
119         save.clear();
120         for(int i=0,a,b;i<E;i++)
121         {
122             scanf("%d%d",&a,&b);
123             G[a].push_back(N+b);
124             G[N+b].push_back(a);
125             save.push_back(make_pair(a,N+b));
126         }
127 
128         st.clear();
129         int match = MaxMatch();
130         //printf("MaxMatch:%d\n",match);
131         for(int i=1;i<=N;i++)
132         {
133             if(Mx[i] != -1) st.insert(make_pair(i,Mx[i]));
134         }
135         int imp = 0;
136         for(auto it = st.begin();it != st.end();it++)
137         {
138             pair<int,int> cur = *it;
139             //printf("delete [%d,%d]\n",cur.first,cur.second);
140             for(int i=0;i<maxn;i++) G[i].clear();
141             for(int i=0;i<save.size();i++) if(save[i] != cur)
142             {
143                 int a = save[i].first,b = save[i].second;
144                 G[a].push_back(b);
145                 G[b].push_back(a);
146             }
147             if(MaxMatch() < match) imp++;
148         }
149         printf("Board %d have %d important blanks for %d chessmen.\n",++cas,imp,match);
150     }
151 }